Porovnání efektivních řešičů úloh lineární elasticity

Abstract

Master thesis deals with mathematical background of advanced methods (algorithms) of combina-tion of direct and iterative solution of large systems of linear algebraic equations obtained by dis-cretisation of linear elasticity problems discretized by finite element method (FEM), which are es-pecially suitable for effective parallel solution of these systems on supercomputers. Namely, the FETI method of decomposition of problem on non-overlaping subdomains and its particular variants were introduced. In theoretical part of the thesis, there was at first introduced the brief mathematical formulation of plane (2D) linear elasticity problem discretised by using FEM and also model 2D lin. elasticity prob-lem, on which the mathematical formulation of particular FETI methods’ variants’ was presented, was defined there. In the next chapter, there were briefly described direct and iterative methods of solving the systems of linear equations and the methods of matrix factorization, used in FETI variants’ algorithms. In the next chapter there were formulated the FETI-1 and TFETI-1 variants’ algorithms, in the next chapter there were defined the (T)FETI-2 variants as (T)FETI-1 variants with deflation applied on CG method solving final systems of equations and the methods of deflation, in the next chapter there was defined the variant FETI-DP and in the last chapter of theoretical there was defined the HTFETI-1. In the practical part of the thesis there were presented and compared the required numerical out-comes from numerical experiments performed on the 2D testing (model) problem of linear elastici-ty, defined in the theoretical part of thesis, for particular variants of the FETI method presented in the theoretical part of the thesis and its subvariants.